Anisotropic intermolecular potentials from an analysis of spectra of H2‐ and D2‐inert gas complexes

Predicted bound states and microwave spectrum of N2-He van der Waals complexes

Numerical calculations show that four modern potential energy surfaces for N(2)-He all support 18 bound intermolecular states for the homonuclear isotopologues (14,14)N(2)-(4)He and (15,15)N(2)-(4)He, and 12 (or 13, for one surface) truly bound states for (14,15)N(2)-He. This contradicts a recent statement [Patel et al., J. Chem. Phys. 119, 909 (2003)] that one of these surfaces supports no bound states, and it yields predictions for 27 allowed pure rotational transitions among the truly bound states of the homonuclear isotopologues of this complex.

Application of direct potential fitting to line position data for the X (1)Sigma(+) and A (1)Sigma(+) states of LiH

A collection of 9089 spectroscopic LiH line positions, of widely varying precision, which sample 84.9% and 98.6% of the A and X state well depths, respectively, have been employed in a direct least-squares fit of the effective potential energy and Born-Oppenheimer breakdown functions for the two states. For the four isotopomers (6)LiH, (7)LiH, (6)LiD, and (7)LiD, the data comprise both pure rotational and vibration-rotational transitions within the ground state, as well as rotationally resolved transitions in the A-X system. Despite the unusual shape and associated anomalous properties of the A state potential, no special features or considerations were required in the direct potential fitting approach. The reduced standard deviation of the fit was close to unity, indicating that the quantum mechanical eigenvalues calculated from the fully analytical functions of the Hamiltonians of the two states, which are characterized by a total of only 53 fitted parameters, represent the line positions, on average, to within the estimated uncertainties. A quantum mechanical calculation of the molecular constants G(nu), B(nu), D(nu), H(nu), L(nu), M(nu), N(nu), and O(nu) from the fitted potential for the A state of (7)LiH confirms that the usual polynomial expansion in J(J+1) is an unsatisfactory representation for the rotational terms of the lowest vibrational levels.

A five-dimensional potential energy surface and predicted infrared spectra for the N2O-hydrogen complexes

We present a five-dimensional potential energy surface for the N(2)O-hydrogen complex using supermolecular approach with the full counterpoise correction at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level. The normal mode Q(3) for the nu(3) antisymmetric stretching vibration of the N(2)O molecule was included in the calculations of the potential energies. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm were employed to calculate the rovibrational energy levels for four species of N(2)O-hydrogen complexes (N(2)O-para-H(2), -ortho-H(2), -ortho-D(2), and -para-D(2)) without separating the inter- and intramolecular vibrations. The calculated band origins are all blueshifted relative to the isolated N(2)O molecule and in good agreement with the experimental values. The calculated rotational spectroscopic constants and molecular structures agree well with the available experimental results. The frequencies and line intensities of the rovibrational transitions in the nu(3) region of N(2)O for the van der Waals ground vibrational state were calculated and compared with the observed spectra. The predicted infrared spectra are consistent with the observed spectra and show that the N(2)O-H(2) complexes are mostly a-type transitions while both a-type and b-type transitions are significant for the N(2)O-D(2) complexes.

A three-dimensional ab initio potential energy surface and predicted infrared spectra for the He–N2O complex

We report a three-dimensional ab initio potential energy surface for He-N(2)O using a supermolecular method at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level. Besides the intermolecular stretching and bending modes, we included the Q(3) normal mode for the nu(3) antisymmetric stretching vibration of N(2)O molecule in order to simulate the observed infrared spectra in the nu(3) region of N(2)O, especially to explain the frequency shift of the band origin in the infrared spectra. The harmonic oscillator approximation is used for the potential curve of the Q(3) mode of the isolate N(2)O molecule. The intermolecular potential energy surfaces are calculated for five potential-optimized discrete variable representation grid points of the Q(3) mode. The three-dimensional discrete variable representation method was employed to calculate the rovibrational states without separating the inter- and intramolecular nuclear motions. The calculated transition frequencies and line intensities of the rotational transitions in the nu(3) region of N(2)O for the van der Waals ground vibrational state are in good agreement with the observed infrared spectra. The calculated band shifts are found to be 0.1704 and 0.1551 cm(-1) for (4)He-N(2)O and (3)He-N(2)O, respectively, which agree well with the observed values of 0.2532 and 0.2170 cm(-1).

Three-dimensional ab initio potential-energy surface and rovibrational spectra of the H2–Kr complex

We report a three-dimensional ab initio potential-energy surface for the H2-Kr complex calculated using a supermolecular method. The electronic calculations were performed at the coupled-cluster singles and doubles level with noniterative inclusion of connected triples levels with a large basis set including midbond functions and the full counterpoise correction for the basis-set superposition error. The intermolecular potential energy between the H2 molecule and the Kr atom were evaluated at five potential-optimized discrete variable representation (DVR) grid points generated from the potential-energy curve of H2. The potential for other bond lengths of H2 could be deduced using polynomial interpolations. The complex is found to have a linear preferred structure with a rather flat energy barrier. The three-dimensional DVR method and the Lanczos propagation algorithm were employed to calculate the rovibrational states without separating the inter- and intramolecular nuclear motions. In addition, the rovibrational spectra from the H2 fundamental vibrational band were calculated. The calculated shift for the band origin is -1.50 cm-1, which is in good agreement with the experimental value of -1.706 cm-1, and the calculated transition frequencies in Q1(0) and S1(0) bands are within 3% of the observed values.

Spectroscopy of Ar–SH and Ar–SD. II. Determination of the three-dimensional intermolecular potential-energy surface

All the pure rotational transitions reported in the previous studies [J. Chem. Phys. 113, 10121 (2000); J. Mol. Spectrosc. 222, 22 (2003)] and newly observed rotation-vibration transitions, P = 1/2 <-- 3/2, for Ar-SH and Ar-SD [J. Chem. Phys. (2005), the preceding paper] have been simultaneously analyzed to determine a new intermolecular potential-energy surface of Ar-SH in the ground state. A Schrodinger equation considering the three-dimensional freedom of motion for an atom-diatom complex in the Jacobi coordinate, R, theta, and r, was numerically solved to obtain energies of the rovibrational levels using the discrete variable representation method. A three-dimensional potential-energy surface is determined by a least-squares fitting with initial values of the parameters for the potential obtained by ab initio calculations at the RCCSD(T)/aug-cc-pVTZ level of theory. The potential well reproduces all the observed data in the microwave and millimeter wave regions with parity doublings and hyperfine splittings. Several low-lying rovibrational energies are calculated using the new potential-energy surface. The dependence of the interaction energy between Ar and SH(2pi(i)) on the bond length of the SH monomer is discussed.

High resolution infrared spectra of H2-Kr and D2-Kr van der Waals complexes

Infrared spectra of weakly bound hydrogen-krypton complexes have been studied at high spectral resolution (0.04 cm(-1)) using a long-path (154 m) low temperature (100 K) absorption cell and a Fourier transform spectrometer. In addition to spectra from the regions of the H(2) and D(2) fundamental vibrational bands in the midinfrared, the results also include the region of the pure rotational S(0)(0) transition of H(2) in the far infrared. A total of 219 measured line positions from these spectra have been fully assigned to specific quantum transitions and form the basis for determining a greatly improved semiempirical three-dimensional intermolecular potential energy surface for hydrogen-krypton in an accompanying paper.

A reliable new three-dimensional potential energy surface for H2–Kr

An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.

Experimental and theoretical study of proton spin-lattice relaxation in H2–Ar gas mixtures: Critical examination of the XC(fit) potential energy surface

Proton nuclear magnetic resonance spin-lattice relaxation time measurements have been carried out at 500 MHz proton Larmor frequency on two hydrogen-argon gas mixtures with 1.90% and 3.93% hydrogen at four different temperatures in the range 225 K < T < 337 K and at two different number densities. The results for different hydrogen mole percentages have been extrapolated to infinite dilution to obtain the contributions to the overall relaxation times arising from the hydrogen-argon interaction. The extrapolated relaxation times fall in the reciprocal regime in which relaxation times are inversely proportional to the density. Relaxation times have also been calculated using quantum mechanical close-coupled computations based on the H2-Ar XC(fit) potential energy surface obtained by Bissonnette et al. [J. Chem. Phys. 105, 2639 (1996)]. Significant differences found between the experimental and theoretical results indicate that the short-range anisotropy of the XC(fit) potential surface is too weak. The reciprocal regime is shown to have a much higher sensitivity to changes in the anisotropic component of the intermolecular potential energy surface.

Uncertainty, Sensitivity, Convergence, and Rounding in Performing and Reporting Least-Squares Fits

This paper describes a procedure for optimal rounding of parameters determined from a linear or nonlinear least-squres fit in order to minimize the number of digits which must be quoted while ensuring that the resulting rounded constants can predict the input data with no significant loss of precision. Related problems concerning nonlinear least-squares convergence and taking account of model dependence of fitted or predicted parameters are also addressed. The recommended rounding procedure is illustrated by applications to electronic band data for the A-X system of I2 and to infrared and microwave data for HF (yielding optimal new Dunham expansion coefficients for ground state HF). An automated version of this sequential rounding procedure has been incorporated in a general subroutine for performing linear or nonlinear least-squares fits. Copyright 1998 Academic Press.